In Review
The results of my 4-trial fractional factorial experiment (main effects) showed that extraction time is the most important variable, and that temperature and C/W ratio are less important. In the interest of completeness this experiment will not simply vary extraction time, but rather seek to efficiently find the maximum.
Lessons from the Screening Experiment
I am accustomed to making my coffee with about 22 fluid ounces of water, which makes two nice cups for my morning. During the screening I used 22 fl oz as a baseline, and increased or decreased the amount of coffee accordingly. The result was that some experiments required 48.8 g of coffee. You can’t possibly imagine how much coffee that is. It almost completely fills a coffee cup with just the beans!
In subsequent experiments I will limit the amount of coffee beans to something more modest, perhaps about 20 g, and vary the amount of water. With this more cautious approach I may live to see the final results.
The Design
NIST offered three designs for response surface objective (RSO) experiments. Specifically there are two interpretations of the Box-Wilson central composite design, each of which requires 20 total runs. An alternative design reduces the number of experiments to 15, which is the reason I chose it.
Specifically, the Box-Behnken design provides an RSO approach for 3 factors in 15 experiments. That is the same number I originally suggested through my naïve approach, but without all the baggage. Effectively, my original 5 values for each factor get reduced to three, and those are shuffled about in a way that is well-suited to estimating their effects. In my case, the specific experiments would be:
| Response Surface Objective | ||||||
|
Actual Values |
Statistics Jargon |
|||||
| Trial |
r (g/ml) |
t (sec) |
T (F) |
R |
T |
T |
| 1 |
0.035 |
10 |
195 |
-1 |
-1 |
0 |
| 2 |
0.075 |
10 |
195 |
+1 |
-1 |
0 |
| 3 |
0.035 |
300 |
195 |
-1 |
+1 |
0 |
| 4 |
0.075 |
300 |
195 |
+1 |
+1 |
0 |
| 5 |
0.035 |
55 |
185 |
-1 |
0 |
-1 |
| 6 |
0.075 |
55 |
185 |
+1 |
0 |
-1 |
| 7 |
0.035 |
55 |
205 |
-1 |
0 |
+1 |
| 8 |
0.075 |
55 |
205 |
+1 |
0 |
+1 |
| 9 |
0.055 |
10 |
185 |
0 |
-1 |
-1 |
| 10 |
0.055 |
300 |
185 |
0 |
+1 |
-1 |
| 11 |
0.055 |
10 |
205 |
0 |
-1 |
+1 |
| 12 |
0.055 |
300 |
205 |
0 |
+1 |
+1 |
| 13, 14, 15 |
0.055 |
55 |
195 |
0 |
0 |
0 |
This set will take me about three weeks. With luck by the time you read this I will have trickled out previous articles, and you will have results in two weeks or less. Sorry for the suspense.
Oh yes, I’m interested in other people’s Q functions too, so if you want to run my exact experiments, please post your data and I will post your results. Public or anonymous, at your discretion.
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One response to “Coffee: Design of the Experiments (Part 2: RSO)”
[…] 20, 2009 I have executed the experiment design discussed Coffee: Design of the Experiments (Part 2: RSO). This “response surface method” experiment design is carefully crafted to provide the […]